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There are two teams I and II of workers at a bridge construction site. Each team consists of W workers. On a particular day, a worker was shifted from team I to team II, if the ratio of the amount of work done by team I in (W + 1) hours and by team II in (W + 2) hours is 10 : 12, respectively, then W is equal to:
1. 24
2. 20
3. 16
4. 18

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Correct Answer - Option 3 : 16

Given:

Number of workers in team I = W

Number of workers in team II = W

New number of workers in team I = W - 1

New number of workers in team II = W + 1

Formula used:

Total work done = Number of workers × Time taken

Calculations:

Total work done by (W - 1) workers in team I = (W - 1)(W + 1)

Total work done by (W + 1) workers in team II = (W + 1)(W + 2)

According to question,

(W - 1)(W + 1)/(W + 1)(W + 2) = 10 : 12

⇒ (W2 - 1)/(W2 + 3W + 2) = 5 : 6

⇒ 6W2 - 6 = 5(W2 + 3W + 2)

⇒ 6W2 - 6 = 5W2 + 15W + 10

⇒ W2 - 15W - 16 = 0

⇒ (W - 16)(W + 1) = 0

(W - 16) = 0 or (W + 1) = 0

⇒ W = 16 or (W + 1) = 0

W ≠ -1

So, W = 16.

∴ The value of W is 16.

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